2) k+k-72
Greatest common factor?

For the first question, we need to find the volume of the region bounded by the paraboloid and the plane. To do this, we can set up a triple integral in cylindrical coordinates as follows:

∫∫∫ ρ dρ dφ dz

where the limits of integration are:

0 ≤ ρ ≤ 2cos(φ)
0 ≤ φ ≤ π/2
(4-ρ²sin²(φ))/4 ≤ z ≤ √(1-ρ²)

For the second question, we need to set up triple integrals in cylindrical coordinates for three different regions:

a) For the region bounded by the sphere and the paraboloid, we can set up the integral as follows:

∫∫∫ ρ dρ dφ dz

where the limits of integration are:

0 ≤ ρ ≤ 2
0 ≤ φ ≤ 2π
0 ≤ z ≤ √(12 - ρ²)

b) For the region in the first octant bounded by the surfaces, we can set up the integral as follows:

∫∫∫ ρ dz dρ dφ

where the limits of integration are:

0 ≤ ρ ≤ 1
0 ≤ φ ≤ π/2
ρ² ≤ z ≤ 1-ρ²

c) For the region inside both spheres, we can set up the integral as follows:

∫∫∫ ρ dρ dφ dz

where the limits of integration are:

0 ≤ ρ ≤ 4sin(φ)
0 ≤ φ ≤ π/2
2-√(16-ρ²) ≤ z ≤ √(16-ρ²)

Note that for all three integrals, we are using cylindrical coordinates, which means we need to express the equations of the surfaces in terms of ρ, φ, and z. Also, we are setting up the integrals but not evaluating them, as instructed in the question.
1. To find the volume of region D bounded by the paraboloid x = y² + z² and the plane x + 4z = 4, set up a triple integral in Cartesian coordinates. First, find the limits of integration for x, y, and z:

- x: x = y² + z² (from paraboloid) and x = 4 - 4z (from plane). Equating both expressions and solving for z, we get z = 0, and x = 4. So, x ∈ [0, 4].

- y: Since it's a paraboloid, y ∈ [-√x, √x].

- z: From the expressions for x, we can find the limits for z as z ∈ [0, x/4].

The triple integral for the volume of region D is:

∫(x=0 to 4) ∫(y=-√x to √x) ∫(z=0 to x/4) dz dy dx

2. Set up triple integrals in cylindrical coordinates for the given regions:

a) Region A:

∫(θ=0 to 2π) ∫(ρ=0 to 2√3) ∫(z=ρ² to √(12-ρ²)) ρ dz dρ dθ

b) Region B (in the first octant):

∫(θ=0 to π/2) ∫(ρ=0 to 1) ∫(z=ρ² to √(1-ρ²)) ρ dz dρ dθ

c) Region C:

∫(θ=0 to 2π) ∫(ρ=0 to 4) ∫(z=2-√(16-ρ²) to 2+√(16-ρ²)) ρ dz dρ dθ

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Answer:

261

Step-by-step explanation:

Answer:

i think its 261

Step-by-step explanation:

Life in the neighborhood depicted in the film "Los Olvidados" is characterized by challenging economic and social conditions.

The neighborhood in "Los Olvidados" is portrayed as a poverty-stricken area where the residents struggle to make ends meet. The film explores the lives of marginalized individuals most particularly young boys, who are caught in a cycle of poverty, violence, and neglect.

The economic conditions in the neighborhood are harsh, with limited opportunities for employment and a lack of access to basic necessities. As a result, the residents are often forced into criminal activities to survive leading to a high level of violence and crime within the community.

Moreover, the social conditions exacerbate the challenges faced by the neighborhood. There is a sense of abandonment and neglect from the government and wider society with little support or resources available to address the issues faced by the residents.

Full question:

Describes life in the neighborhood that takes place in the film Los Olvidados by Luis Buñuel, taking into account their economic and social conditions through the different activities carried out by the neighborhoods.

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Answer:

angle y = 60

Step-by-step explanation:

They are equal due to the rule that vertical angles are always equal

"A pair of vertically opposite angles are always equal to each other."

hope this helps

The final thickness of the sheet is  = 0.0669 cm

brasses are copper zinc alloys. In general, they have good strength and corrosion resistance, although their structure and properties are a function of zinc content , Alloys containing up to approximately 35% zinc are single phase alloys, consisting of a solid solution of zinc and alpha copper

% cold reduction = (initial thickness - final thickness )  × 100

                                                  initial thickness

        0.30%       =            (0.0955cm - final thickness ) ×  100            

                                                     0.0955cm

             final thickness    =     0.0669cm

Brass in an alloy of copper and zinc, bonze is an alloy containing 80% of cropper. A fuses mass of brass and bronze is found to contain 74% . Brass, alloy of copper and zinc, of historical and enduring importance because of its hardness and workability

Hence the final thickness of sheet is 0.0669 cm

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Answer:

Area of a parallelogram is base times height. Note that CD = AB & AD = BC

to find the height, draw a line from angle B perpendicular to the base b. Lets call the point of intersection at the base E. This constitutes a right triangle with AB as the hypotenuse. Using the law of sine to calculate the height h:

h/sin(A) = AB/sin(90°) ( sin(90°) = 1)

h = AB * sin(45°)

h = 10 * sin(45°)

Area = 14 * 10 * sin(45°) = 140 * sin(45°) ≈ 98.99 QEDexplanation:

Answer:

The volume of the 2 and 1/4 box is 729/64 cubic inches.

Step-by-step explanation:

Volume of a Box

What is the volume of a 2 and 1/4 box

To calculate the volume of a box, you need to multiply its length, width, and height together. If the box has dimensions of 2 and 1/4, we need to convert the mixed number to an improper fraction.

2 and 1/4 = 9/4

Let's assume that the dimensions of the box are in inches. So, if the length of the box is 2 and 1/4 inches, its length in inches would be 9/4 inches.

Similarly, let's assume that the width and height of the box are also 2 and 1/4 inches, which means their measurements in inches would also be 9/4 inches.

Now we can calculate the volume of the box as:

Volume = Length x Width x Height

Volume = (9/4) x (9/4) x (9/4)

Volume = 729/64 cubic inches

Answer:

4

Step-by-step explanation:

Because 2 x 2 = 4 :>

The maximum limit to add the videos or images in Carousel is 10MB and the aspect ratio to add the images or videos is 1:1

There are many applications that are present where the videos and images can be added in the websites. The maximum images in the in few website is nine, but in carousel is 10MB of size and also it can be added up to 1:1 ratio of aspect size. The Carousel also allows the user to add slides and images. It helps to add the graphical representation.

The size of the videos must be from 60 seconds to 30 seconds of size and also the video includes the visual templets that help the user to have the presentation in an effective ways. There are many templets that also helps the  user to present in a professional way.  The carousel is a cloud representation that helps to create the slideshow online and also present it in the blockage videos. The online photos and images can also be added.

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Answer:

121. three digits. 121/11=11

Step-by-step explanation:

Answer:

90.

Step-by-step explanation:

1000 / 11

= 90.9.

Answer:

x = 12

Step-by-step explanation:

The attached figure shows the measures of the angles. Here, line a is parallel to line b.

Given that,

m∠3 = 128 and m∠6 = (10x + 8)

We need to find the value of x.

Here,

\(\angle 3 =\angle 6\) (alternate interior angles)

So,

\(10x+8=128\\\\10x=128-8\\\\10x=120\\\\x=12\)

So, the value of x is 12. Hence, the correct option is (D).

Answer:

-2x > 6, so x < -3

So A is correct.

Answer:

45?????

Step-by-step explanation:

i think

give me a heart for trying

The matrix that represents the matrix D is \(\left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-3&11\end{array}\right]\)

Given the elements of the matrix C.

The matrix c is represented by its rows and columns element, and the arrangements are:

C11 = 3    C12 = 1   C13=-9   C14 = 8

C21 = 2   C22=2   C23 =0   C24 = 5

C31 = 16   C32 = 1  C33=-3   C34=11

Remove the matrix name and position

3  1  9  8

2 2  0  5

16  1  -3  11

Represent properly as a matrix:

\(C = \left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-3&11\end{array}\right]\)

Matrix C equals matrix D.

So, we have:

\(D = \left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-3&11\end{array}\right]\)

Hence, the matrix that represents matrix D is \(\left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-3&11\end{array}\right]\)

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Answer:

y = 5/9x + 19/3

Step-by-step explanation:

slope: 10 - 5 / 6 - (-3) = 5/9

point-slope form:

y - 5 = 5/9(x + 3)

y -5 = 5/9x + 4/3

y = 5/9x + 6 1/3

Answer:

609

Step-by-step explanation:

ratio of teachers to students at Priory School =2:27

Let X= total number of both the students and the teacher

Ratio of teacher=( 2/29)X

Ratio of student is (27/29 )X

But total number of teacher = 42

2/29 ×X =42

2X= 42×29

2X=1218

X= 609

Hence, school's total population is 609

Answer:

Unfortunately, Monday's figure is missing. The mean is 6 hours. Sunday . Monday Tuesday Wednesday Thursday Friday ? hours 5 hours 6 hours.

Answer:

y=7x+6

Step-by-step explanation:

hope i helped

The solid figure that has 8 edges and four triangular faces is a pyramid.

The restricted value on the range of function f(x) is given as follows:

3.

From the horizontal dashed line, the function never assumes a value of y = 3, hence the restricted value on the range of function f(x) is given as follows:

3.

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Answer:

3

Step-by-step explanation:

The range of a function is the set of all possible output values (y-values).

The given diagram shows the graph of a rational function with a horizontal asymptote at y = 3 (indicated by the dashed line).

An asymptote is a line that the curve gets infinitely close to, but never touches.

Therefore, as there is an asymptote at y = 3, the curve of the function will never touch the line y = 3, and consequently the value of y = 3 is restricted from the range of the function.

For the given linear equation we have:

Here we have a linear equation:

4x -10y = 20

First, let's find the y-intercept, this is the point with x = 0, so evaluating in that we get:

4*0 - 10y = 20

-10y = 20

y = 20/-10

y = -2

The x-intercept is what we get by evaluating in y = 0.

4x - 10*0 = 20

x = 20/4

x = 5

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The present value of the annuity at the end of year 7 is approximately $47,069.08.

To calculate the present value of an ordinary annuity, we can use the formula:

PV = PMT * [(1 - (1 + r)⁻ⁿ) / r],

where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, the annual payment is $4,500, the interest rate is 8%, and the number of periods is 16. However, the payments start at the end of year 8 and continue until the end of year 23, which means there is a delay of 7 years.

Using the formula, the present value at the end of year 7 can be calculated as:

PV = $4,500 * [(1 - (1 + 0.08)⁻¹⁶) / 0.08] = $47,069.08.

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Answer:

99

Step-by-step explanation:

You can solve it by Squaring/multiply 18 by itself and 15 by itself then subtract them both:

(18 × 18) - (15 × 15)

324 - 225

99

You could also do difference of two squares:

(x² - y²)

= (x + y) (x - y)

= (18 + 15) (18 - 15)

= (33) (3)

= 99

Answer:

Step-by-step explanation:

Evaluate

= (18)^2-(15)^2

= 324 - 225

= 99

To solve the problem, we need to first convert the given information into minutes. We know that Haley spends 90 minutes doing her homework, which is equivalent to 1 and 1/2 hours. We also know that 2/3 of an hour is equivalent to 40 minutes (since 1 hour is 60 minutes, and 2/3 of 60 is 40). Finally, eight minutes is already in minutes.

Therefore, the total time Haley spends on homework, reading, and making her lunch is:

We cannot determine how many more minutes Haley spends on reading since we don't have any information about it.

Answer:

42 minutes

Step-by-step explanation:

Haley spends = 90 minutes

for reasoning = 2/3 of an hour = 2/3 * 60 = 40 minutes

further time = 8 minutes

total time consumed = 40 + 8 = 48 minutes

time left to spend with reading and making her lunch = 90 - 48

= 42 minutes

Answer:

Step-by-step explanation:

48

Answer:

51

Step-by-step explanation:

Pythagorean theorem

a^2+b^2=c^2

45^2+24^2

2025+576

2601=c^2

square root both sides

51=c

Hopes this helps please mark brainliest

Answer:

16

Step-by-step explanation:

The trapezoidal rule is a numerical integration method that frequently overestimates the real value of a function's definite integral.

The trapezoidal rule is a strategy for approximating the definite integral in calculus. The trapezoidal rule works by computing the area of the region under the graph of the function f(x) that is approximated as a trapezoid. The trapezoidal rule is commonly used to calculate the area under curves. This is achievable if the overall area is divided into smaller trapezoids rather than rectangles. The Trapezoidal Rule integration determines the area by approximating the area under a function's graph as a trapezoid. The midway rule uses rectangular areas to approximate the definite integral, whereas the trapezoidal rule uses trapezoidal approximations to approximate the definite integral. Simpson's approach works by first approximating the original function with piecewise quadratic functions.

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The measure of \($\angle CAB = 180^{\circ} - \angle ACD$\)

What is the circumscribed circle?

A circumscribed circle is a circle that is drawn around a polygon such that the circle touches all the vertices of the polygon. In other words, the vertices of the polygon lie on the circumference of the circle.

Given that a circle is circumscribed around a quadrilateral ABCD, it is clear that the circle passes through all four vertices of the quadrilateral, A, B, C and, D. Also, the diameter of the circle is the diagonal AC of the quadrilateral.

The angles formed by the diameter with the tangents from the non-adjacent vertices are supplementary. That is \($\angle CAB + \angle ACD = 180^{\circ}$\)

Therefore, the measure of \($\angle CAB = 180^{\circ} - \angle ACD$\)

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